TrendLSW: Trend and Spectral Estimation of Nonstationary Time Series in R

TL;DR

TrendLSW is an R package that offers wavelet-based tools for analyzing nonstationary time series, including spectrum estimation, trend detection, and confidence interval calculation, with boundary handling for arbitrary data lengths.

Contribution

The package introduces novel wavelet-based methods for spectral and trend estimation in nonstationary data, with boundary handling that eliminates the need for data pre-processing.

Findings

Effective spectral estimation in nonstationary series

Accurate trend detection with wavelet thresholding

Boundary handling enables analysis of arbitrary data lengths

Abstract

The TrendLSW R package has been developed to provide users with a suite of wavelet-based techniques to analyse the statistical properties of nonstationary time series. The key components of the package are (a) two approaches for the estimation of the evolutionary wavelet spectrum in the presence of trend; and (b) wavelet-based trend estimation in the presence of locally stationary wavelet errors via both linear and nonlinear wavelet thresholding; and (c) the calculation of associated pointwise confidence intervals. Lastly, the package directly implements boundary handling methods that enable the methods to be performed on data of arbitrary length, not just dyadic length as is common for wavelet-based methods, ensuring no pre-processing of data is necessary. The key functionality of the package is demonstrated through two data examples, arising from biology and activity monitoring.